This invention relates generally to magnetic resonance imaging (MRI), and more particularly the invention relates to reconstruction of partially parallel encoded MRI data using anti-aliasing, hereinafter referred to as APPEAR.
In magnetic resonance imaging (MRI), it is well known that multiple receiver coils can be used to reduce the gradient encoding required and, consequently, the time needed to acquire an image. This is because multiple receiver coils enable the image to be encoded in parallel—at each sample time each receiver collects a differently encoded datum. The acquired data are the result of encoding with both the gradients and the spatial sensitivity of the receiver coils (coil sensitivities) and no longer correspond to samples in a common k-space.
Over the past few years, many reconstruction methods that take advantage of sensitivity encoding have been developed and improved. The original SMASH method [D. K. Sodickson and W. J. Manning, “Simultaneous acquisition of spatial harmonics (SMASH): fast imaging with radiofrequency coil arrays,” Magn. Reson. Med., vol. 38, no. 4, pp. 591-603, 1997.] is limited to Cartesian k-space trajectories and places requirements on the coil sensitivity functions that are difficult to achieve in practice. SENSitivity Encoding (SENSE) theory [K. P. Pruessmann, M. Weiger, M. B. Scheidegger, and P. Boesiger, “SENSE: sensitivity encoding for fast MRI,” Magn. Reson. Med., vol. 42, no. 5, pp. 952-62, 1999.], [K. P. Pruessmann, M. Weiger, P. Bornert, and P. Boesiger, “Advances in sensitivity encoding with arbitrary k-space trajectories,” Magn. Reson. Med., vol. 46, no. 4, pp. 638-51, 2001.] relaxes the requirement that the coil sensitivities have specific profiles and provides an iterative method for reconstructing arbitrary k-space trajectories. The SPACE-RIP [W. E. Kyriakos, L. P. Panych, D. F. Kacher, C. F. Westin, S. M. Bao, R. V. Mulkern, and F. A. Jolesz, “Sensitivity profiles from an array of coils for encoding and reconstruction in parallel (SPACE RIP),” Magn. Reson. Med., vol. 44, no. 2, pp. 301-8, 2000.] method allows non-iterative reconstruction for k-space trajectories which do not fall on a Cartesian grid in one dimension, while the recently introduced PARS method [E. N. Yeh, C. A. McKenzie, M. A. Ohliger, and D. K. Sodickson, “Parallel magnetic resonance imaging with adaptive radius in k-space (PARS): constrained image reconstruction using k-space locality in radiofrequency coil encoded data,” Magn. Reson. Med., vol. 53, no. 6, pp. 1383-92, 2005.] can reconstruct one, two and three dimensional arbitrary k-space trajectories without iteration. All of the above methods require the coil sensitivity functions to be found to a high degree of accuracy. Finding the coil sensitivities can be accomplished by performing a full field-of-view (FOV) initial calibration scan before acquiring the image data [K. P. Pruessmann, M. Weiger, M. B. Scheidegger, and P. Boesiger, “SENSE: sensitivity encoding for fast MRI,” Magn. Reson. Med., vol. 42, no. 5, pp. 952-62, 1999.] or by designing the k-space trajectory such that a low resolution full FOV scan can be extracted from the acquired data [C. A. McKenzie, E. N. Yeh, M. A. Ohliger, M. D. Price, and D. K. Sodickson, “Self-calibrating parallel imaging with automatic coil sensitivity extraction,” Magn. Reson. Med., vol. 47, no. 3, pp. 529-38, 2002.]. In practice it is difficult to obtain the coil sensitivity functions without errors and, even when small errors exist in the coil sensitivity functions used in the reconstruction process, these errors can lead to visible image artifacts.
PILS [M. A. Griswold, P. M. Jakob, M. Nittka, J. W. Goldfarb, and A. Haase, “Partially parallel imaging with localized sensitivities (PILS),” Magn. Reson. Med., vol. 44, no 4, pp 602-9, 2000.] is a non-iterative method that does not require the coil sensitivities to be known with great accuracy and works with arbitrary k-space trajectories. However, the PILS method is only viable when the coil sensitivities are sufficiently localized in space.
GRAPPA [M. A. Griswold, P. M. Jakob, R. M. Heidemann, M. Nittka, V. Jellus, J. Wang, B. Kiefer, and A. Haase, “Generalized autocalibrating partially parallel acquisitions (GRAPPA),” Magn. Reson. Med., vol. 47, no. 6, pp. 1202-10, 2002.], as well as predecessors AUTO-SMASH [P. M. Jakob, M. A. Griswold, R. R. Edelman, and D. K. Sodickson, “AUTO-SMASH: a self-calibrating technique for SMASH imaging. Simultaneous Acquisition of Spatial Harmonics,” Magma, vol. 7, no. 1, pp. 42-54, 1998.] and VD-AUTO-SMASH [R. M. Heidemann, M. A. Griswold, A. Haase, and P. M. Jakob, “VD-AUTO-SMASH imaging,” Magn. Reson. Med., vol. 45, no. 6, pp. 1066-74, 2001.], uses an autocalibration technique that does not require the coil sensitivities to be known and avoids problems in coil sensitivity estimation that affect the previous methods. For Cartesian trajectories, autocalibration is able to remove the aliasing artifacts caused by reduced gradient encoding. While the autocalibration technique has been extended to specific non-Cartesian trajectories [M. A. Griswold, R. M. Heidemann, and P. M. Jakob, “Direct parallel imaging reconstruction of radially sampled data using GRAPPA with relative shifts,” in Proc. Eleventh ISMRM, 2003, p2349.], [K. A. Heberlein, Y. Kadah, and X. Hu, “Segmented spiral parallel imaging using GRAPPA,” in Proc. Twelfth ISMRM, 2004, p. 328.], [K. A. Heberlein and X. Hu, “Auto-calibrated parallel imaging using dual-density spirals,” in Second International Workshop on Parallel MRI, 2004.], in doing so, it loses some of its ability to successfully remove all of the aliasing artifacts.
We develop a new calibration technique which we call the local projection calibration technique. We show that this new technique is able to remove the aliasing artifacts from arbitrary k-space trajectories, without needing to estimate the coil sensitivity functions. The autocalibration technique as used by GRAPPA for Cartesian trajectories is a special case of the local projection calibration technique.
In their development of SENSE theory [K. P. Pruessmann, M. Weiger, M. B. Scheidegger, and P. Boesiger, “SENSE: sensitivity encoding for fast MRI,” Magn. Reson. Med., vol. 42, no. 5, pp. 952-62, 1999.], Pruessmann et al. provide a general formulation for encoding with coil sensitivities. We extend the linear algebra framework of SENSE to develop the local projection calibration technique. Using this linear algebra framework, we show that the local projection calibration technique is fundamentally different from techniques that use low resolution images to construct coil sensitivity estimations. Moreover, the local projection calibration technique avoids the main difficulties in estimating coil sensitivities from low resolution data: Gibbs ringing distortion and an inability to deal with sensitivity maps with high frequency content.
The present invention is directed to magnetic resonance image reconstruction and non-iterative method using a combination of gradient encoding and receiver coil sensitivities, but does not require coil sensitivity functions and can be used with arbitrary k-space trajectories. A local projection calibration technique removes aliasing artifacts caused by reduced gradient encoding.